Earlier this week, Jolie told PEOPLE exclusively that she was adopting her second child, a newborn Ethiopian baby orphaned by AIDS, which has killed more than 900,000 people in the African nation.
"Her name is Zahara," Jolie told PEOPLE. Arrangements for the adoption had been expected to be completed by mid-week.
The 30-year-old actress and U. N. activist said that the girl's full name is Zahara Marley Jolie. Although Jolie declined to divulge the child's age, weight or height, she did tell PEOPLE that she and Maddox, whom she adopted from a Cambodian orphanage in 2002, are "very happy to have a new addition to our family."
Jolie had often talked of adopting a second child. After a trip to Ethiopia earlier this year, Jolie said of Maddox: "My son is in love with Africa, so he has been asking for an African brother or sister."
"Angie's over the moon," a source close to the actress told PEOPLE. "It's a dream come true. She's always wanted to extend her family."
The source also denied rumors that Jolie and Pitt are planning a family together. "This has nothing to do with her relationship with Brad Pitt. People are going to try to say it's about their relationship. But it's not. Angelina's adopting as a single mother, and she wants that emphasized."